Fast computation in adaptive tree approximation

Authors:
Peter Binev;Ronald DeVore
Affiliations:
University of South Carolina, Department of Mathematics, USA;University of South Carolina, Department of Mathematics, USA
Venue:
Numerische Mathematik
Year:
2004

Citing 0
Cited 2

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Abstract

Adaptive methods of approximation arise in many settings including numerical methods for PDEs and image processing. They can usually be described by a tree which records the adaptive decisions. This paper is concerned with the fast computation of near optimal trees based on n adaptive decisions. The best tree based on n adaptive decisions could be found by examining all such possibilities. However, this is exponential in n and could be numerically prohibitive. The main result of this paper is to show that it is possible to find near optimal trees using computations linear in n.